Classification of Curtis-Tits and Phan amalgams with 3-spherical diagram

2016/11/03 by Blok, Rieuwert J., Hoffman, Corneliu G., Shpectorov, Sergey V.
#20D05 #20E06 #20F05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1611.01038

Abstract

We classify all non-collapsing Curtis-Tits and Phan amalgams with 3-spherical diagram over all fields. In particular, we show that amalgams with spherical diagram are unique, a result required by the classification of finite simple groups. We give a simple condition on the amalgam which is necessary and sufficient for it to arise from a group of Kac-Moody type. This also yields a definition of a large class of groups of Kac-Moody type in terms of a finite presentation.

Related

• Realizations and properties of 3-spherical Curtis-Tits Groups and Phan groups
• A classification of Curtis-Tits amalgams
• Curtis-Tits Groups of simply-laced type
• Uncountably many 2-spherical groups of Kac-Moody type of rank 3 over \mathbbF₂
• Spherical objects in dimensions two and three